(defconstant *input-data*
  '( 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
     49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
     81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
     52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
     22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
     24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
     32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
     67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
     24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
     21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
     78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
     16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
     86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
     19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
     04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
     88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
     04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
     20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
     20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
     01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48))
(defparameter col-length 20)
(defparameter row-length 20)

(defconstant *euler11-data* 
			 (make-array '(20 20) :initial-contents
			 '((08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08)
               (49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00)
               (81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65)
               (52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91)
               (22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80)
               (24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50)
               (32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70)
               (67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21)
               (24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72)
               (21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95)
               (78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92)
               (16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57)
               (86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58)
               (19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40)
               (04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66)
               (88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69)
               (04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36)
               (20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16)
               (20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54)
               (01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48))) )

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 
;;; This solution can be simplified by using Array, @see forum Page 8 

;;; right
(defun rule-1 ()
  (loop for r from 0 to (1- row-length)
    maximizing (loop for c from 0 to (- col-length 4)
		      maximizing (let ((data-position (+ c (* r col-length))))
							  (reduce '* *input-data* :start data-position :end (+ data-position 4))))))

;;; down
(defun rule-2 ()
  (loop for r from 0 to (- row-length 4)
    maximizing (loop for c from 0 to (1- col-length)
		      maximizing (let ((data-position (+ c (* r col-length))))
						      (* (nth data-position *input-data*)
								 (nth (+ data-position (1- col-length)) *input-data*)
								 (nth (+ data-position (* 2 (1- col-length))) *input-data*)
								 (nth (+ data-position (* 3 (1- col-length))) *input-data*))))))

;;; right diagonally
(defun rule-3 ()
  (loop for r from 0 to (- row-length 4)
    maximizing (loop for c from 0 to (- col-length 4)
		      maximizing (let ((data-position (+ c (* r col-length))))
						      (* (nth data-position *input-data*)
								 (nth (+ data-position (1- col-length) 1) *input-data*)
								 (nth (+ data-position (* 2 (1- col-length)) 2) *input-data*)
								 (nth (+ data-position (* 3 (1- col-length)) 3) *input-data*))))))
;;; left diagonally
(defun rule-4 ()
  (loop for r from 0 to (- row-length 4)
    maximizing (loop for c from (1- col-length) downto 4
		      maximizing (let ((data-position (+ c (* r col-length))))
						      (* (nth data-position *input-data*)
								 (nth (- (+ data-position col-length) 1) *input-data*)
								 (nth (- (+ data-position (* 2 col-length)) 2) *input-data*)
								 (nth (- (+ data-position (* 3 col-length)) 3) *input-data*))))))


;(format t "~a~%" (time (max (rule-1) (rule-2) (rule-3) (rule-4))))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; another simpier brute force solution
;;; TODO 
;;; a. define variable inside DO for next-right-col-position, next-row-position, next-left-col-position
;;; 
(defun euler11 (&optional (rule-op '*) (result-op 'max))
  (loop for i from 0 to 19
		maximizing (loop for j from 0 to 19
						 maximizing (do ((k 0 (1+ k))
										 (right 1 (funcall rule-op right (if (array-in-bounds-p *euler11-data* i (+ j k)) (aref *euler11-data* i (+ j k)) 0)))
										 (down 1 (funcall rule-op down (if (array-in-bounds-p *euler11-data* (+ i k) j) (aref *euler11-data* (+ i k) j) 0)))
										 (right-g 1 (funcall rule-op right-g (if (array-in-bounds-p *euler11-data* (+ i k) (+ j k)) (aref *euler11-data* (+ i k) (+ j k)) 0)))
										 (left-g 1 (funcall rule-op left-g (if (array-in-bounds-p *euler11-data* (+ i k) (- j k)) (aref *euler11-data* (+ i k) (- j k)) 0))))
									    ((= k 4) (funcall result-op right down right-g left-g k))))))

(format t "~a~%" (time (euler11)))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; code from euler forum
;;; Page 2, 7
(defun p11pvec (ix iy dx dy)
  (do ((p 1 (* p (if (array-in-bounds-p *euler11-data* y x) (aref *euler11-data* y x) 0)))
	   (x ix (+ x dx)) 
	   (y iy (+ y dy)) 
	   (c 0 (1+ c))) 
	  ((= c 4) p)))

(defun p11 ()
  (let ((mx 0))
    (dotimes (x 20)
      (dotimes (y 20)
        (setf mx (max mx
                     (p11pvec x y 1 0)
                     (p11pvec x y 0 1)
                     (p11pvec x y 1 1)
                     (p11pvec x y -1 1)))))
   mx)) 

;(format t "~a~%" (time (p11)))
